High School Mathematics-Physics SMILE Meeting 1997-2006 Academic Years Mechanics: Resonance

10 February 1998 Karlene Joseph [Lane Tech HS]
She brought in a project based on the book Why the toast  lands jelly side down? by Robert Ehrlich [Princeton 1997] ISBN 069-1028877.

"Make the rings by cutting 5 strips of construction paper of width several centimeters and lengths, and lengths 15 cm, 20 cm, 25 cm, 30 cm, and 35 cm. Tape the two ends of each strip to make a circular ring and then tape each ring to a transparent base, so that the rings stand vertically next to one another in order from smallest to largest."

She constructed circular strips of paper and taped them on a overhead sheet. The sheet was shaken and the resonance of each was excited at a certain rate. There was a problem in that there were a number of frequencies that excited rings, and it seemed that the rings responded to a number of frequencies.  But harmonics caused various responses, hiding the true resonance. She used rings in increments of 5 cm. It seems that a different multiple might give better individual responses.

```       <--shaken-->***
*** but not stirred!```

10 February 1998 Larry Alofs [Kenwood HS]
Description of a 1973 Summer Project on resonance done with Jim Williams.

He described using a 1957 Ford blower motor to show resonance. He used a DC motor with a disk and something to cause it to be out of balance--in this case it was a screw placed on what was a squirrel cage made with only one disk left--and with a variable power source to vary the speed: i.e. the frequency of the vibration.

Now attach this to a 2" x 4" x 8' board on one end and clamp the other to the table, at lower speeds the board will flex perpendicular to the wide side, and as speed is increased it will stop vibrating and as it still increased the board will vibrate in the axis of the wide side. Thus we can show the resonance of the board in each direction.

CENCO makes a speaker like device that could also cause a vibration, but his is a lot less expensive.

Comment by Porter: In 1831 cavalry troops were marching in step across the Broughton Bridge near Manchester England, when the bridge collapsed.  Since then, marching soldiers have been ordered to break step (not to march in cadence) when crossing bridges. Marching in step to one of the natural frequencies of vibration of a bridge can cause the bridge to absorb energy cumulatively from marching troops, resulting in bridge damage or destruction. For a quantitative discussion of resonance in bridge collapse, see http://www.riverdeep.net/current/2000/08/082900t_bridge.jhtml.

28 April 1998  Arlyn Van Ek [Illiana Christian High School]
He brought in a long piece of wood trim [rectangular cross-section, with thick and thin sides] with a DC motor attached to one end, which was driven at various rotational rates by varying the input voltage. At lower speeds [frequencies] he obtained the resonances for "transverse vibration" of the rod [motion in the direction of thin side], which was clamped to the at the other end. With higher frequencies he obtained the "longitudinal vibration" of the rod [motion in direction of thick side]. Arlyn also have a "mechanical resonance" device for measuring the frequency of vibration by looking at the resonant motion of one of the internal masses.

Comment by Larry Alofs [Kenwood Central HS]
He said that this system [and many other ones] have the property known as a "tipped resonance curve", in that the resonance amplification factor [gain] is asymmetric with respect to increasing and decreasing frequencies. He said that such a property arises because of non-linearity in the mechanical system, according to one of his instructors.

27 March 2001: Val Williams Jr (Bass School) Traveling Sounds
We listened carefully to the ticking of a timer that his son, Val III, held up

• Terry Donatello helped Val III by asking questions, and established that sound from the clock gets to our ears by traveling through the air.
• When we wrapped the timer in a newspaper and put everything inside a box, we could still hear the ticking.
• We put the timer on the table, and put our ear on the table.  We could still hear the ticking through the table.
• We put the timer inside a metal can, and closed the lid.  We could hear it.
• We put the timer inside a paper bag, and could still hear it.

The conclusion is that sound travels through air, as well as wood or plastic (the table), paper, and cardboard.  The volume and the quality of the sound were changed under these various conditions.  Karlene Joseph suggested holding the timer against the window, as well as against the chalkboard, to show dramatic changes in the volume of sound.  A discussion of resonators to produce the sensation of sound through vibrations, with applications for the hard-of-hearing, followed.  Our eardrum system is an excellent resonator!

01 May 2001 Richard Goberville  (Joliet Central HS, Physics) Resonance

• He attached three weighted strings of various lengths to a rod, and moved the rod side-to-side at a certain rate in order to cause one pendulum to move rather dramatically, while the others hardly moved at all.  A pendulum moves because of the resonance produced when the frequency of motion is identical with the natural frequency of that pendulum.
• Richard asked why a tuning fork that resonates at a natural frequency f is also resonant at frequency f/2.  The answer is that frequency f/2 [wavelength 2l] is also a resonant frequency, but not frequency 2f [wavelength l/2].
• There was discussion of circumstances in which one could add energy to a swing.  In general, an external force F acting on a mass moving with velocity v adds energy at the  rate P = F · v.  In other words, one adds energy to a system by applying a force to an object in the direction of motion of the object.
• Handout: Trick of the Trade; Resonating Blow-Pipe Drum from The Physics Teacher, [http://www.aapt.org/] Vol 39, No 3 (March 2001).  He had made the drum out of sturdy cardboard tube, a short length of plastic pipe, and a sheet of rubber film.  He hummed into the tube (like a Kazoo) and we saw a paper clip dance wildly on the surface of the drum when a particular frequency was excited, but not otherwise.

05 February 2002: Earl Zwicker (IIT, Physics) String Blow Pipe
Earl
showed each of us a plastic "pipe" with a string loop attached to one end, which he had obtained years ago from a fast food outlet.

The pipe pretty much had the shape of a conventional tobacco pipe, with stem and bowl.  But the bowl had an opening at its bottom end, as well as its top.  The continuous loop of string passed through the holes, entering at the bottom and leaving at the top.  When Earl blew air into the pipe stem, the air came out of the top of the bowl, but not the bottom (because the bowl was designed that way).  The string --- which was very light and fuzzy --- was carried along in the air stream.  It took the shape of an elongated loop, leaving the bowl at its top and turning around to re-enter at its bottom.  Simple enough! But wait!

Earl pointed out that, near the very top of the loop there was a small "depression", or "valley".  How come?  This question was thrown out for our consideration.

It may be related to the similar indentation that occurs on a broad, flat belt in an old-fashioned machine shop, in which the power from one master motor is transferred by the belt to a long shaft.  Pulleys along the shaft are then used with other belts to drive machines located at various positions to the shaft.

Interesting! What do you think?

05 March 2002: Don Kanner gave Earl some articles and a video demonstration concerning the "dimple" in the belt mentioned by Earl in the SMILE meeting of 05 February 2002..   Earl will look at them, to see if the effect is the one he mentioned, and whether the explanation is reasonable.

06 May 2003: Arlyn Van Ek [Iliana Christian HS]        Resonance Show
Arlyn
partially filled a wine glass with water, held it by the stem with one hand, wet his finger on the other hand, and rubbed it around the rim.  This set up a stick-slip motion, which produced a fairly high-pitched sound, in the kiloHertz range.  He poured some water out of the glass and repeated the process, producing a higher pitched sound.  As he continued to pour water out of the glass, the pitch continued to increase.  How come?  Earl Zwicker reminded us that the frequency f of oscillation of a mass m attached to a spring of spring constant k is given by f = 1/(2 p) Ö(k/m). Earl suggested that -- analogously-- the effective spring constant k is determined by the oscillations at the rim of the glass. Since one can clearly see the water vibrating inside the glass, the effective mass m includes water, so that m decreases as the amount of water in the glass decreases.  Hence the frequency increases as the glass is emptied. Very nice!

Arlyn then showed a video tape of a Washington DC street musician, who was very proficient in playing tunes, using a different glass for each note.  He did a rather impressive job on Ode to Joy, Chorus of 9th Symphony 4th Movement by Ludwig van Beethoven [http://www.all-about-beethoven.com/symphony9.html], as well as various sailing tunes.  This particular street musician was quite talented, and several of us asked Arlyn to make copies of the performance. For more information see How Can You Make a Wine Glass Sing?http://www.howstuffworks.com/question603.htm.

Arlyn continued by demonstrating resonance using a kit of solid Singing Rods, available for about \$20 from Arbor Scientifichttp://www.arborsci.com/detail.aspx?ID=491Arlyn held a rod at its center, and produced a high-pitched sound that increased in intensity as he rubbed the rod by grasping it between forefinger and thumb and sliding [rubbing] them along the length of the rod [stick-slip motion with his fingers].  When he held it at 2/3 and 3/4 of its length,  still higher pitches were produced.  The sound was produced by resonant longitudinal oscillations of the rod, with a vibrational node at the holding point.  The sound was not spectacularly loud, unless you hold the rod at a node corresponding to a normal mode of vibration of the rod --- in which case it really wakes everybody up!

Pretty physics, Arlyn!

06 May 2003: John Bozovsky [Chicago Design Academy -- the school formerly known as Bowen HS -- Physics]       Vibrating String Apparatus Revisited
John
showed us a vibrating string apparatus made out of a cast-off battery operated electric razor, which was attached to a board.  A string was connected to the razor head, and tied at its other end to a Pinch Clamp, which would normally be used in the lab for closing rubber hose.  The pinch clamp was also attached the board, so that the tension in the string could be adjusted by turning the adjustable screw in the pinch clamp.  The razor vibrated at a fixed frequency f of about 100 Hz, as estimated from the hum of the razor.  The length L of the string was fixed at about 30 cm.  By varying the tension, various standing wave patterns could be produced. As the tension T was decreased, the speed of vibrations on the string decreases, and the wavelength l also decreases. Thus, one can fit more nodes on the string of length L, since n l = 2 L, n = 1, 2, 3.  See the writeup for Ann Brandon in the previous class.  This is a cool system, without doubt!

John also showed us a home-made, Adjustable Resonance Tube Apparatus, in which the height of a column of water is varied by raising a reservoir filled with water, with rubber tubing attached to a nipple at the bottom of the tube, as well as to one at the bottom of the reservoir. This device is a variation of the commercially available devices available from science supply houses  We heard the resonant sounds very well!

Plunk your magic twanger, Froggy [http://michelesworld.net/dmm/frog/gremlin/memory.htm] --- er, John! You were in tune with the physics!